Linear free energy of activation relationship for barrierless association reactions

An analysis of variational transition state theory rate constants, for the association reactions Cl^- + CH₃-Cl, Cl^- + CH₃Br, H+ CH₃, H+ diamond {111}, CH₃ + CH₃, and Al + Al₂ shows that the free energy of activation ΔG varies nearly linearly with temperature, over a broad temperature range, for each reaction. This suggests that association rate constants can be parametrized by the free energy of activation at 300 K, ΔG₃₀₀/(+), and the change in ΔG(+) with temperature, ΔΔG(+)/ΔT. The near linear dependence of ΔG(+) with temperature is supported by a semiempirical model for association kinetics. The rate constants for Cl^- + CH₃Cl, Cl^- + CH₃Br, and CH₃ + CH₃ decrease with increase in temperature, while those for H + CH₃, H + diamond{111}, and Al + Al₂ slightly increase. For the six association reactions considered here, the linear free energy relationship gives semiquantitative rate constants over a rather broad temperature range of 200-2000 K. To calculate accurate rate constants over a broader temperature range, particularly at low temperatures, nonlinear terms must be included in the free energy expansion.